What does the Riegel formula actually do?

The Riegel formula is an empirical fit to race-distance scaling: t2 = t1 · (d2/d1)^1.06. The exponent 1.06 was published by Pete Riegel in 1977 from athletic data. Above 1 it means time grows slightly faster than distance — doubling the distance more than doubles the time. It is a curve fit to averages, not a physiological model.

When does it overestimate or underestimate?

Riegel tends to over-predict (give a slower time than you would actually run) when the target distance is much longer than the known one and the runner has good endurance — because the constant 1.06 is averaged across a population whose long-distance fade varies a lot. It under-predicts when the known race was a sprint and the target is also short, because anaerobic effort scales differently from aerobic.

Why is the formula different for sprints vs. endurance?

Sprints (≤ 800 m) are limited by anaerobic power and biomechanics; endurance races (≥ 5 km) by aerobic capacity, fuel, and pacing discipline. Riegel was fit on endurance data and is reliable from roughly 1500 m up to a half-marathon. Outside that band the underlying physiology stops looking like a single power-law, and the prediction degrades.

Why are marathon predictions from a 5K time often wrong?

A 5K is a 15–25 minute effort dominated by VO₂max; a marathon is a 3–5 hour effort dominated by glycogen, hydration, pacing, and the wall. The factor between the two distances is ≈ 8.4×, well past Riegel's reliable range. Most 5K → marathon Riegel predictions are 5–15 % too fast for runners who haven't built the endurance base — which is why the calculator flags long extrapolations as unreliable.

How should I use this prediction in training?

Treat it as a ceiling, not a target. If Riegel says 1:50 for your half-marathon goal, train at the paces that support that effort — but plan to race by feel and split, not by chasing the predicted time blindly. The prediction assumes you have done the specific endurance work for the target distance.

HEAHealth & Fitness

Race Time Predictor

Predict your race time at a target distance using the Riegel formula. Enter a recent race or workout (distance + time) and a target distance — get the predicted time and pace, plus a warning when the extrapolation crosses into territory where Riegel becomes unreliable.

Distance unit

Both distances use the same unit.

Known distance

Time (hours)(optional)

Time (minutes)(optional)

Time (seconds)(optional)

Target distance

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How It Works

Formula

t_2 = t_1 \cdot \left(\frac{d_2}{d_1}\right)^{1.06}

Where

$t_1$: Known time(seconds)
$d_1$: Known distance(km or mi)
$t_2$: Predicted time(seconds)
$d_2$: Target distance(km or mi)

Enter a known race time at a known distance, then the target distance. The calculator applies the Riegel formula t2 = t1 · (d2/d1)^1.06 to estimate the time at the target distance, and divides by the target distance to give the average pace.

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